Corresponding Angle Axiom|Theorems

Consecutive Interior Angles and Corresponding Angles Axiom

Lines And Angles|Linear Pair Axioms|Theorem (Vertically Opposite Angles)|Axioms (Corresponding Angles)|Theorem 1 (Alternate Interior Angles)|Theorem 2 (Alternate Interior Angles)

Transversal; Corresponding Angles and Alternate Interior Angles

In Fig. 5.2, a pair of corresponding angles is

Axioms and Theorem

Some Basic Definition-Collinear And Non Collinear Points |Angles & Its Types|Complementary And Supplementary Angles|Relation Between Two Angles-Adjacent Angles|Linear Pair Of Angles,Vertically Opposite Angles|Axioms |Theorem |Transversal |Corresponding Angles,Alternate Interior Angles,Co-interior Angles

Read the following statements which are taken as axioms (i) If a transversal intersects two parallel lines, then corresponding angles are not necessarily equal. (ii) If a transversal intersect two parallel lines, then alternate interior angles are equal. Is this system of axioms consistent ? Justify your answer.

Property 2 Pairs of corresponding angles are equal.

Corresponding angles a pair of angles in which one arm of both the angles is on the same side of the transversal and their other arms are directed in the same sense is called a pair of corresponding angles.

If two triangles have their corresponding angles equal, are they always congruent? If not, draw two triangles which are not congruent but which have their corresponding angles equal